BOSTON — After an extraordinary outpouring by angry employees, the board of directors of the Market Basket supermarket chain said Friday that it would consider offers to buy the chain, including one from the ousted president, Arthur T. Demoulas.

The company has been in turmoil for more than a week as thousands of employees walked off their jobs and held rallies, including one Friday that drew an estimated 10,000 people, demanding that Arthur T., as he is known, be reinstated. His rival and cousin, Arthur S. Demoulas, fired him last month in the latest twist in a decades-old family feud over control of the company, founded by their grandfather.

The labor action has led to bare shelves in many of the chain’s 71 stores in New England and to the firing of some of the top managers who organized the rebellion. And shoppers have boycotted the chain, which analysts say must be losing millions of dollars.

Arthur T. Demoulas said this week that he had made a bid to buy 50.5 percent of the company. The amount was not disclosed, but the company, one of the region’s most successful supermarket chains, is reported to have had revenue of $4.6 billion in 2013. The board of directors met Friday and issued a statement confirming the bid. “The board will evaluate and seriously consider this proposal, along with any other offers previously received and to be received,” the statement said. “Following its evaluation of all of the offers, it will convey its recommendations to the company’s shareholders.”

The board also made clear that it was not ceding to the workers’ demand that Arthur T. Demoulas be reinstated, noting that it had reaffirmed the hiring of the two executives who took his place.

Gary N. Chaison, a professor of industrial relations at Clark University in Worcester, Mass., said he thought management’s strategy was to “play the waiting game,” with the expectation that the revolt would fizzle. No one knows how this will end, he said, but the main question facing the company is whether it can regain the public trust.

Michael A. Roberto, a professor of management at Bryant University in Smithfield, R.I., said the board’s statement that it would consider Arthur T. Demoulas’s bid was meaningless since it had a fiduciary responsibility to consider all bids, especially given the chain’s diminishing value. Still, he suggested that someone like the investor Warren Buffett might be able to buy it, but only if he rehired Arthur T. Demoulas to run it.

A version of this article appears in print on , on Page A14 of the New York edition with the headline: Grocer Is Open to Buyers’ Bids Amid Turmoil. Order Reprints | Today’s Paper | Subscribe